What is the equation of the following graph in vertex form

Question

parabolic function going down from the left through the point zero comma five and turning at the point two comma one and continues

Answer 1

The equation of a parabola is a quadratic.  Use the vertex form:

 

y = a(x-h)² + k  where "a" is a constant (to be determined) and (h,k) is the location of the vertex.  The problem tells you the location of the vertex, (h,k) = (2,1) so the equation is:

 

y = a(x-2)² + 1

 

Now we just need to find the value of a.  To find a, plug in the x and y values of the point that's given, (0,5), and solve for a:

 

y = a(x-2)² + 1

5 = a(0-2)² + 1

Can you finish it from here?

Answer 2

Vertex is (2,1) according to your information.  In general, V(h,k).

 

Equation must be y - k =a(x-h)² for any quadratic function (parabola). Furthermore, you know that (0,5) is a point on the curve, so substitute for h, k, x and y to  determine what coefficient "a" has to be.